In this paper, we employ some weaker forms like $\mathcal{R}$ -completeness, $\mathcal{P}$ -closedness, and $\mathcal{R}$ -continuity while achieving the same results as presented by different authors. Furthermore, we have introduced and analyzed rational-type $\mathcal{R}$ -contractions, establishing their corresponding fixed point results within the proposed framework. To validate our findings, we present examples in which our results hold, whereas the corresponding results from existing literature do not, thereby illustrating the robustness and wider applicability of our approach. Additionally, the proposed framework ensures stability in both market equilibrium and economic growth through fractional differential equations, emphasizing its relevance to production-consumption models.
